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Abstract

We have examined the possibility of determining the optical
properties of a two-layer medium by using a diffusion approximation
radiation transport model [Appl. Opt. 37, 779
(1998)]. Continuous-wave and frequency-domain (FD)
low-noise Monte Carlo (MC) data were fitted to the
model. Marquardt–Levenberg and a simulated annealing algorithm
were used and compared as optimization techniques. Our particular
choice of optical properties for the two-layer model was consistent
with skin and underlying fat in the presence of an exogenous
chromophore [Appl. Opt. 37, 1958 (1998)]. The
results are therefore specific to this set of optical
properties. It was found that the cw diffusion solution could never
be used to estimate all optical properties reliably. The combined
cw and FD solutions could not be used to estimate some of the top-layer
optical properties to an accuracy of better than 10%, although the
absorption and the transport scattering coefficients of the bottom
layer could be estimated to within 7% and 0.5%, respectively. No
improvement was found from simultaneously fitting MC data at three
different modulation frequencies. These results point to the need
for a more accurate radiation transfer model at small source–detector
separations.

References

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a The number of reflectance measurements
included in the fits was the same as in all other cases (12), but
they were made at ρ = 1–6 (increment 1), 8–16 (increment
2), and 20 mm. Despite the large number of function evaluations,
SA-t gave poor quality parameter estimates. The true parameters gave
χ2(t) = 19,400.

Table 8

As in Table 6 but for a Modulation Frequency
f = 300 MHz [χ2(t) =
80.3]

Parameters

Mrqrt-t

Error (%)

SA-f

Error (%)

μa
1
/mm-1

6.843 × 10-2

11.70

6.999 × 10-2

9.69

μs
1
′/mm-1

1.691

-13.46

1.692

-13.57

μa
2
/mm-1

7.279 × 10-3

-3.98

7.256 × 10-3

-3.66

μs
2
′/mm-1

1.005

-0.46

1.006

-0.64

l/mm

1.433

4.47

1.414

5.73

χmin2

8.93

8.93

Evaluations

1584

200,001

Table 9

As in Table 6 but for a Modulation Frequency
f = 1 GHz and SA-t Shown Instead of SA-f
[χ2(t) = 1010]

a The number of reflectance measurements
included in the fits was the same as in all other cases (12), but
they were made at ρ = 1–6 (increment 1), 8–16 (increment
2), and 20 mm. Despite the large number of function evaluations,
SA-t gave poor quality parameter estimates. The true parameters gave
χ2(t) = 19,400.

Table 8

As in Table 6 but for a Modulation Frequency
f = 300 MHz [χ2(t) =
80.3]

Parameters

Mrqrt-t

Error (%)

SA-f

Error (%)

μa
1
/mm-1

6.843 × 10-2

11.70

6.999 × 10-2

9.69

μs
1
′/mm-1

1.691

-13.46

1.692

-13.57

μa
2
/mm-1

7.279 × 10-3

-3.98

7.256 × 10-3

-3.66

μs
2
′/mm-1

1.005

-0.46

1.006

-0.64

l/mm

1.433

4.47

1.414

5.73

χmin2

8.93

8.93

Evaluations

1584

200,001

Table 9

As in Table 6 but for a Modulation Frequency
f = 1 GHz and SA-t Shown Instead of SA-f
[χ2(t) = 1010]